DETROIT (AP) — Detroit Mayor Dave Bing was elected to replace a scandal-plagued predecessor after promising to clamp down on crime. But following allegations of a sex scandal involving another police chief, he’s having trouble stabilizing the department, let alone the streets.

Bing suspended Police Chief Ralph Godbee, 44, after a subordinate, a 37-year-old internal affairs officer, claimed the two had engaged in a sexual relationship for about a year.

The mayor hired Godbee two years ago after firing his predecessor, in part because of similar charges involving a subordinate. Bing knew at the time that Godbee previously had a romantic relationship with the same woman, a police lieutenant.

Should Bing’s investigation conclude that Godbee too must go, the city would be forced to seek its fifth police chief in four years. In Bing’s three-plus years in office, he already has fired two chiefs.

“He’s had more people resign, fired, quit than any other mayor that I know of,” Councilman Kwame Kenyatta said Wednesday. “It either says he chooses the wrong people or doesn’t know how to choose the right people.”

Like many police departments, Detroit’s force is under severe financial constraints. The city has about 2,700 officers, down from 4,000 a decade ago.

The department reports most violent crimes numbers are down this year, but the city also is on track to eclipse last year’s 344 murders. Robberies at gas stations and convenience stores, including the assault and carjacking of a prominent church pastor earlier this year, are becoming more violent and brazen.

“The officers are working 24/7 and aren’t being treated well,” said Oakland County Commissioner William Dwyer, a former Detroit police official. “They’ve taken dramatic cuts in salaries and benefits. They are in the most dangerous city right now in the U.S. If you expect them to perform, you ought to treat them like professionals and not second-class citizens.”

Even before the alleged scandal came to light, Bing and Godbee have been at odds with officers over a 10 percent pay cut, requirements that they pay more for health care and new rules requiring 12-hour work days.

Earlier this year, the chief reduced staffing inside police precincts to get more officers on the city’s crime-plagued streets.

“The more immediate issue facing people in Detroit are the screaming headlines about the number of people shot or injured, and the fact that the number seems to be on the increase as opposed to the decrease,” said Sheila Cockrel, a political analyst and former Detroit councilwoman. “Detroiters are going to want a police chief focusing on those issues and not what’s happening in his personal life.”

Angelica Robinson, the internal affairs officer who says she had a relationship with Godbee, posted on Twitter a photo of herself with her service weapon in her mouth, her attorney David Robinson said. She had learned Godbee was at a weekend police conference with another woman, said the attorney, who is not related to Angelica Robinson.

He said Godbee had other officers locate her and put her under surveillance. She has since been reassigned from internal affairs to other duties and does not have use of her service weapon, David Robinson said.

On Tuesday, Bing said in a statement that he suspended Godbee for 30 days from his $140,400-a-year post “pending a full and thorough investigation of this matter.”

Godbee, returning to Detroit after attending a police conference out of state, told reporters Wednesday evening at Detroit Metropolitan Airport that he could not comment on Angelica Robinson’s claims or his suspension.

Bing has spent much of his first term as mayor cleaning up the fiscal mess and $300 million budget deficit left by ex-mayor and convicted felon Kwame Kilpatrick. He’s also changed the perception of a City Hall warped by public corruption.

However, his handling of the police department has been spotty, Kenyatta said, pointing to the firing of ex-chief Warren Evans that led to Godbee getting the job.

Bing appointed, Evans, a former Wayne County sheriff, as police chief in 2009 but fired him after he took part in a promotional video for a cable police reality show. Bing later said he also fired Evans because the chief was romantically involved with Lt. Monique Patterson.

Godbee also had a romantic relationship with Patterson before she began dating Evans and when she was Godbee’s subordinate.

The relationship between Godbee and Patterson was made public after Godbee was named interim chief. Bing subsequently issued a statement insisting he wouldn’t fire Godbee for having an affair with a subordinate.

At the time of his firing, Evans was spearheading an apparently successful police blitz on crime hot spots across the city.

Godbee joined the department in 1987 and rose to assistant chief in 2007. He later retired only to be reappointed assistant chief in July 2009 when Evans was hired.